Associated to a linearised action of the reductive group \(G\)  on \(Y\) , there is a GIT instability, or HKKN, stratification of \(Y\)  due to work of Kempf [1]} and Hesselink [2]}. It also agrees with a symplectic Morse-theoretic stratification associated to the norm square of the moment map for the action of the maximal compact subgroup of \(G\)  [3]}, [4]}.
